Question

The solution of $\frac{dy}{dx}=\frac{ax+b}{cy+d}$ represents a parabola if

• A. $a=0,c=0$
• B. $a=1,b=2$
• C. $a=0,c\ne 0$
• D. $a=1,c=1$

Answer 1

The correct option is C $a=0,c\ne 0$

The given equation is with separable variables so (cy + d)dy = (ax + b)dx. Integrating we have $\frac{c{y}^2}{2}+dy+K=\frac{a{x}^2}{2}+bx,K$ being the constant of integration. The last equation represents a parabola if $c=0,a\ne 0$ or $a=0,c\ne 0$